The present invention relates generally to methods and systems for the a, precise calibration of instruments. More specifically, the present invention pertains to an accurate and efficient process for calibrating accelerometers.
An accelerometer is a transducer used for measuring acceleration. Acceleration is usually measured at a measurement point in the accelerometer, along a sensitive axis of the accelerometer. Generally, the magnitude of an applied acceleration is communicatively coupled to external instruments or circuits as an electrical impulse having amplitude proportional to the magnitude of the applied acceleration. The electrical impulse comprises the measured acceleration and is processed by the external circuits as required for a variety of applications. One such application is, for example, an Inertial Measurement Unit (IMU), where acceleration measurements are used to generate velocity and positioning information.
The electrical impulse output of an accelerometer is proportional to the acceleration, applied at the measurement point along the sensitive axis of the accelerometer. The process of calibrating an accelerometer consists of computing a constant of proportionality, referred to as a scale factor of the accelerometer. The scale factor of an accelerometer precisely relates the amplitude of the electrical impulses comprising the measured acceleration to the magnitude of a corresponding acceleration applied at the measurement point, along the sensitive axis of the accelerometer.
A multi-axis accelerometer device can measure acceleration along multiple sensitive axes. This can be a combination of one or more accelerometers, with one or more axes of sensitivity each, and a common frame of reference with respect to which each of these accelerometers and their respective measurement points and sensitive axes remains fixed at all times. The frame of reference of the multi-axis accelerometer device is the coordinate system in which the acceleration sensed by the array is measured. The frame of reference of the array is typically an orthogonal frame of reference.
The process of calibrating a multi-axis accelerometer device consists of computing the scale factors for each of the multiple sensitive axes in the device, and furthermore computing the alignment angles of the sensitive axes in the device with respect to a frame of reference of the device. One measure of the alignment angles of a sensitive axis of the device is the direction cosine vector or alignment vector of this sensitive axis of the accelerolmeter device with respect to the orthogonal frame of reference of the array. The alignment vector of a sensitive axis of the multi-axis accelerometer device is the unit vector in the direction of the sensitive axis of the device. For optimal precision of measurement using the multi-axis accelerometer device, it is desirable to calibrate the multi-axis accelerometer device by precisely determining the scale factors and alignment angles corresponding to each individual sensitive axis of the device.
Prior art systems for calibrating accelerometers (e.g., measuring and defining the scale factor) relied on comparisons of the accelerometers to certain standard devices. Such prior art systems necessarily assume that the standard devices themselves are properly calibrated, often leading to the introduction of additional error into the calibration process. For example, one prior art system (see prior art U.S. Pat. No. 5,970,779) requires the use of precisely controlled swing arm motor systems to which the accelerometer being tested is mounted, along with an appropriate counter weight. The swing arm motor would be precisely controlled by a processor to impart a simple harmonic motion acceleration to the sensitive axis of the accelerometer, and vary this acceleration by varying the angular acceleration of the swing arm. The resulting output of the accelerometer would be examined with respect to the controlled varying of the swing arm motor, and the scale factor would be determined therefrom.
One problem with the above prior art approach is that it requires a precisely controllable motor for varying the angular velocity of the accelerometer. The motor needs to precisely apply a simple harmonic acceleration to the accelerometer by varying the angular velocity about an axis of rotation. As described above, this system requires the proper calibration of the standard devices themselves (e.g., the motor), which often leads to additional error in the calibration of the accelerometer.
A second, more important drawback of the above prior art approach is that it requires measuring the radius of rotation of the accelerometer. This distance can be very difficult to measure accurately, since the measurement point of the accelerometer is internal to the accelerometer. Any error in this measurement will manifest itself in through a flawed calibration.
Thus, what is required is a solution that accurately measures and determines the scale factor and alignment angles of each of the multiple sensitive axes in the device simultaneously. What is required is a solution that calibrates the multi-axis accelerometer device without introducing unnecessary sources of error. The required solution should be precise and avoid reliance on standard devices, which can introduce error into the calibration process. The required solution should not rely on any time varying control of a standard device to impart variable acceleration. The required solution should not rely on measurements of distance to points internal to the accelerometer. The present invention provides a novel solution to the above requirements.
The present invention provides a solution that accurately measures and determines the scale factor and alignment angles of multiple sensitive axes of a multi-axis accelerometer device simultaneously. The present invention provides a solution that calibrates a multi-axis accelerometer device without introducing unnecessary sources of error. The solution of the present invention is precise and avoids reliance on standard devices, which can introduce error into the calibration process. The solution of the present invention does not rely on any time varying control of a standard device to impart variable acceleration.
In one embodiment, the present invention is Implemented as a spectral method for simultaneously determining respective scale factors and alignment vectors of a multi-axis accelerometer device for measuring acceleration. The scale factors and alignment angles are determined simultaneously in one process, allowing the calibration of the multiple axes of the multi-axis accelerometer device in one process. To measure the scale factors and alignment angles, the multi-axis accelerometer device to be calibrated is mounted on a turntable. The turntable has a tilt angle with respect to a vertical axis defined by the local gravity vector. The turntable is used to spin the multi-axis accelerometer device around an axis of rotation at an angular velocity such that each sensitive axis of the device experiences a time varying component of the local gravity vector (e.g., due to the tilt angle). The respective outputs of the multiple sensitive axes of the multi-axis accelerometer device are logged as each sensitive axis in the array experiences the time varying component of the local gravity vector. This process is repeated with the multi-axis accelerometer device placed in each of three orthogonal orientations along the axes of the frame of reference of the array (e.g. the orthogonal X, Y and Z axes of the frame of reference).
The scale factors and alignment vectors of the sensitive axes of the multi-axis accelerometer device are determined by combining the recorded outputs of the multiple sensitive axes of the device mathematically with the a predicted output of an ideal accelerometer (e.g., a sine wave). Herein, the predicted output is based on the tilt angle, the angular velocity of the ideal accelerometer and on gravitational acceleration. This combination is performed after the multi-axis accelerometer device has been placed on the turntable in each of three orthogonal orientations along the axes of the frame of reference of the device. In so doing, the present invention accurately measures and determines the scale factor and alignment angles of the sensitive axes of the device, without relying on any time varying control of a standard device (e.g., stepper motor, etc.) to impart variable acceleration to the multi-axis accelerometer device. It also does not rely on a measurement of the radius about which the multi-axis accelerometer device rotates, and thereby, does not rely on a precise knowledge of the location of measurement point of the device internal to the device.